Time is a dangerous toy in “Harry Potter and the Cursed Child,” the enthralling two-part play about the later life of its title wizard. Various characters in this deluxe London import, which opened on Sunday night at the Lyric Theater, find it in their power to journey into the past, which means altering the future, which means serious trouble for everyone.

In that regard, these stumbling adventure-seekers must be regarded as lesser magicians than their creators, who include J.K. Rowling, the writer of the prodigiously popular Harry Potter fantasy novels, and the poetic director John Tiffany (“Black Watch,” “The Glass Menagerie”). This inspired team bends time to its will with an imagination and discipline that leave room for nary a glitch, making five hours of performance pass in a wizardly wink of an eye.

Featuring a script by Jack Thorne — from an original story by Ms. Rowling, Mr. Thorne and Mr. Tiffany — “Harry Potter and the Cursed Child” also gives vibrant, decades-traversing life to those wistful “what if” speculations about the past that occupy both grown-ups and children. It’s a process that involves folding stories into stories into stories, collapsing years into minutes and making dreams feel eternal, and more vivid than reality.

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Jamie Parker, left, as Harry Potter, and Sam Clemmett as Albus Potter, in a GIF created by a series of images.CreditSara Krulwich/The New York Times

If you give yourself over to this show’s hypnotic powers — and I’m talking to the parents who may be accompanying their Potter-mad offspring with reluctance — you’ll find everything that happens onstage seems as improbably fluid as, well, time itself. It helps that what happens includes some of the most eye-boggling illusions you’ll ever witness, without a visible wire or trap door in sight.

In embodying the magical with such seeming spontaneity, “Cursed Child” becomes the new gold standard for fantasy franchise entertainment on Broadway. By contrast, most of the family-courting stage versions of animated films that have ruled the theater district for so long look as stiff and artificial as parades of windup toys.

The budget for “Cursed Child,” which has been a sold-out hit in London since opening there in 2016, is a staggering $68 million, the most ever spent on a nonmusical Broadway production. Yet I mean it as the highest praise when I say that the show doesn’t look expensive.

Or rather, it seems expensive only in the way of a custom-made little black dress, one with endless tricks up its deceptively simple sleeves. “Cursed Child,” which has a deeply symbiotic cast of 40, shimmers with beguiling richness, but you’re never conscious of its seams or the effort that’s gone into the making of it.

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Sam Clemmett, center, as Albus Potter, practicing his spells.CreditSara Krulwich/The New York Times

This effect is evident as soon as you step into the lobby of the Lyric Theater, which has been transformed from a too big, ungainly show barn into a cozy yet sumptuously appointed environment that seems to have been exactly as it is for many, many years. On the stage, open for your inspection, looms the vaulted central hall of Harry Potter’s alma mater, Hogwarts School of Witchcraft and Wizardry.

This stately mansion is the work of the ace set designer Christine Jones and has been shrouded in beckoning, velvety and inventively concealing shadows by Neil Austin’s lighting. The scenery at this point consists mostly of suitcases and trunks. But watch out for the gliding staircases that will soon become a crucial part of the mise en scène.

Luggage and staircases are appropriate motifs for a show that turns out to be all about traveling, in the broadest sense of the word, and unpacking the conflicted feelings that are part and parcel of the long-distance journey of growing up. Overseeing everything from above, like an inescapable eye, is a palely glowing clock.

Beneath this formidable timepiece, a series of scenes melt into one another, approximating cinematic cross-cutting, while managing to feel both epic and intimate. The story begins where the final novel in the Potter series, “Harry Potter and the Deathly Hallows,” ended.

Harry (an irresistibly anxious Jamie Parker) is an adult now (which doesn’t mean he has entirely grown up), employed by the Ministry of Magic, which is run by his old school chum (and partner in fighting the forces of darkness), Hermione Granger (the marvelous Noma Dumezweni). Harry and his wife, Ginny (Poppy Miller), are seeing their sons off to school from King’s Cross Station in London.

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Anthony Boyle, center left, as Scorpius Malfoy, and Brian Abraham as the Sorting Hat.CreditSara Krulwich/The New York Times

It will be the first year at Hogwarts for their younger boy, Albus (Sam Clemmett), who is understandably ambivalent about going to the place where his student father became “the most famous wizard in the whole world.” Hermione and her prankster husband, Ron Weasley (Paul Thornley, delightful) are there, too, with their daughter, Rose (Susan Heyward).

Also on the platform: the platinum-haired Draco Malfoy (Alex Price), once Harry’s sinister rival, and his nerdy son, Scorpius (Anthony Boyle, who leads with his adenoids in a show-stealing performance). Scorpius and Albus are destined to bond, both as outcasts in the young wizarding world and as allies in a quest that may lead them into the realms once occupied by the ultimate dark lord, Voldemort.

Their insular friendship, which opens up enough to include a determined young woman named Delphi Diggory (Jessie Fisher), will be sorely tested, as will their contentious relationships with their dads. And yes, the script has more variations on father issues than the entire canon of Greek tragedy.

Part of the generation-crossing appeal of Ms. Rowling’s novels lies in her ability to give operatic grandeur to the most universal and pedestrian hopes and fears — feelings harbored by anguished adolescents of all ages — by placing them in a wildly fantastical context. (In this sense, her fiction resembles that of Stephen King.) And this show more than honors that dichotomy.

That everyone who sees “Cursed Child” is implored to “keep the secrets” relieves me of the onerous burden of parsing the byzantine but only occasionally tedious plot. Those who have read the Potter novels, or seen the blockbuster film adaptations, should not feel that the carefully appointed logic of Ms. Rowling’s fictional prototype has been violated.

The uninitiated may be confused when the mere mention of certain names (Dolores Umbridge, Neville Longbottom) draws gasps from the audience. But I can’t imagine anyone ultimately not feeling strangely at home within the show’s magical flux.

This state of enchantment is sustained through Steven Hoggett’s balletic movement direction of the large ensemble and Katrina Lindsay’s wittily transformative costumes. Working with Ms. Jones and Jamie Harrison (credited with illusions and magic), they summon an alternate universe of a world gone fascist, for the show’s darkest and most uneasily topical sequences. And do watch out for the phantasmal Dementors.

The leading cast members, most of whom I first saw in London, have relaxed into looser but completely detailed performances. (Mr. Parker, Ms. Dumezweni and Mr. Thornley cut loose delightfully to portray their characters as inhabited by young’uns.) It is impossible not to identify with most of the people — and creatures — onstage, who memorably include a fabulous centaur (David St. Louis) and that great, giggling ghost of the first-floor girls’ bathroom, Moaning Myrtle (Lauren Nicole Cipoletti).

For this slyly manipulative production knows exactly how, and how hard, to push the tenderest spots of most people’s emotional makeups. By that I mean the ever-fraught relationships between parents and children, connections that persist, often unresolved, beyond death.

Time-bending, it turns out, has its own special tools of catharsis in this regard. In the multiple worlds summoned here, it is possible for kids to instantly become their grown-up mentors, and for a son to encounter his forbidding father when dad was still a vulnerable sapling.

“I am paint and memory,” a talking portrait of the long-dead wizard Dumbledore (Edward James Hyland) says to his former star pupil, Harry. Well, that’s art, isn’t it? Substitute theatrical showmanship for paint, and you have this remarkable production’s elemental recipe for all-consuming enchantment.